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Theorem isfin2 8663
 Description: Definition of a II-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin2 FinII []
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem isfin2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pweq 4006 . . . 4
21pweqd 4008 . . 3
32raleqdv 3057 . 2 [] []
4 df-fin2 8655 . 2 FinII []
53, 4elab2g 3245 1 FinII []
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1374   wcel 1762   wne 2655  wral 2807  c0 3778  cpw 4003  cuni 4238   wor 4792   [] crpss 6554  FinIIcfin2 8648 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ral 2812  df-v 3108  df-in 3476  df-ss 3483  df-pw 4005  df-fin2 8655 This theorem is referenced by:  fin2i  8664  isfin2-2  8688  ssfin2  8689  enfin2i  8690  fin12  8782  fin1a2s  8783
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